In vehicles such as automobiles, idle stop is the known control to stop an engine at a stop of the vehicle and restart the engine at a start of the vehicle, so as to reduce fuel consumption and emission during the vehicle stop. In relation to this idle stop control, there are various known techniques on engine restart control to restart the engine when the booster negative pressure of the brake system or the battery capacity satisfies a predetermined condition after an engine stop. For example, the cited document 1 discloses the technique of restarting the engine when the booster negative pressure of the brake system is reduced by a predetermined ratio after a stop of the engine. The cited document 2 discloses the technique of restarting the engine when the booster negative pressure of the brake system decreases below a threshold value after a stop of the engine.